Methods and systems for determining an enhanced rank order value of a data set

ABSTRACT

The value of a median or other rank of interest in a dataset is efficiently determined. Each active bit of the dataset is serially processed to compute one bit of the output value from each bit of the input dataset. If any sample in the dataset has an active bit that differs from the determined output value for that bit, then that sample can be marked as no longer in consideration. After an active bit has been processed, the data for that bit may be discarded or subsequently ignored. These techniques allow the rank value to be efficiently determined using pipelined logic in a configurable gate array (CGA) or the like. Further implementations may be enhanced to compute clipped means, to identify “next highest” or “next lowest” values, to reduce quantization errors through less-significant bit interpolation, to simultaneously process multiple values in a common pipeline, or for any other purpose.

PRIORITY CLAIM

This application is a continuation-in-part of U.S. application Ser. No.12/608,374 entitled “METHODS AND SYSTEMS FOR PROCESSING DATA USINGNON-LINEAR SLOPE COMPENSATION” filed on Oct. 29, 2009, which isincorporated herein by reference.

GOVERNMENT RIGHTS

This invention was made with United States Government support underContract Number HQ0276-08-C-0001 with the Missile Defense Agency. TheUnited States Government has certain rights in this invention.

TECHNICAL FIELD

The following discussion generally relates to digital filteringtechniques and systems. More particularly, the following discussionrelates to a rank order filter that may be used to determine the valueof a median or other particular rank of a data set.

BACKGROUND

A rank order filter identifies the value of a particular rank in a setof data. A median filter, for example, is one type of rank order filteridentifies the value that is in the midpoint of a dataset; that is, thevalue that equally divides the remaining values in the set such thathalf are larger and half are smaller than the median value. Other rankorder filters may be used to identify values at different ranks withinthe dataset (e.g., bottom 25%, top 25%, etc.), as desired.

Many different types of median and other rank order filters have beenwidely used over many years in a multitude of settings. In signalprocessing applications, for example, it is often desirable to be ableto perform some kind of noise reduction on an image or signal. Themedian filter is one type of nonlinear digital filtering technique thatis often used to remove noise. Since the median function is notconcerned with the particular values of outlying data, the medianfunction can be very effective at ignoring the effects of relativelylarge magnitude noise within the dataset. For this reason, medianfiltering is very widely used in digital image processing because, undercertain conditions, the median function preserves image edges whileremoving noise from the image. Median filters, as well as other types ofrank order filters, are widely used in other applications as well.

Most current rank order filters, however, can demand relativelysignificant computing resources to provide accurate results within thetime frames needed for certain applications. In particular, it can becomputationally challenging to implement a rank order for a relativelylarge dataset, particularly using field programmable gate arrays orsimilar hardware logic devices. It is therefore desirable to provide arank order filter that reliably yet efficiently identifies the value ofa particular rank in a data set, such as the median value. These andother desirable features and characteristics will become apparent fromthe subsequent detailed description and the appended claims, taken inconjunction with the accompanying drawings and this background section.

BRIEF DESCRIPTION

Methods and systems are described to determine the value of a median orother rank of interest in a set of data samples. In various exemplaryembodiments, each active bit of the data is sequentially processed tocompute one output bit of the output value. The output bit is suitablydetermined for each active bit by comparing a count of the data sampleshaving a particular value with the relative number of the rank beingsought. If the comparison determines that the output for that active bitis the same as the particular value, then all data samples having adifferent value for the active bit can be excluded from furtherconsideration. Although the various techniques and systems may beimplemented in any manner, various embodiments allow the value of amedian or other rank of interest to be determined efficiently using afield programmable gate array (FPGA) or other specialized hardware.

Various embodiments provide methods executable by data processinghardware to find an output value of a desired rank in a set of datasamples, wherein each of the data samples comprises a set of digitalbits each having either a first value or a second value. The exemplarymethod suitably includes the steps of receiving each of the data samplesin the data set at the data processing hardware computing one bit of theoutput value for each active bit in the set of digital bits. Thecomputing performed for each active bit suitably comprises determiningthe active bit of the output value based upon a comparison of thedesired rank with a count of the data samples having the first value,excluding all data samples having the second value for the active bitfrom further consideration if the comparison indicates that the activebit of the output value is the first value, and adjusting the desiredrank to exclude all data samples having the first value for the activebit from further consideration if the comparison indicates that theactive bit of the output value is the second value. After computing theoutput bits for each active bit, outputting the output value from theoutput bits computed for each active bit.

Other embodiments provide computational systems to find an output valueof a desired rank in a set of data samples, wherein each of the datavalues comprises a set of digital bits each having either a first valueor a second value. The system suitably comprises an output interface anddata processing circuitry configured to receive the set of data samplesand to compute the output value to include one output bit from eachactive bit in the set of digital bits. The computing suitably comprises,for each of the active bits, determining a count of the number of datasamples that remain in play and that have the active bit equal to thefirst value. If the count is not less than the desired rank, theproviding the second value as the output bit for the active bit andtreating each of the data samples having the active bit equal to thefirst value as no longer in play. If the count is less than or equal tothe desired rank order, providing the first value as the output for theactive bit, treating each of the data samples having the active bitequal to the second value as no longer in play, and adjusting thedesired rank to account for the data samples that are no longer in play.The output value is then provided from the output bits provided for eachactive bit via the output interface.

The various implementations may be enhanced or modified in manydifferent ways to create any number of equivalent embodiments. Variousother embodiments, aspects and other features are described in moredetail below.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

Exemplary embodiments will hereinafter be described in conjunction withthe following drawing figures, wherein like numerals denote likeelements, and

FIG. 1 is a block diagram of an exemplary data processing system thatimplements certain types of rank order filters;

FIGS. 2A-B are flowcharts showing exemplary processes for finding anoutput value of a particular rank of a dataset;

FIGS. 3A-B show examples of how multi-stage processing can be used tofind a value of a desired rank within a set of data samples;

FIG. 4 is a flowchart showing an exemplary process for finding a “nexthighest” value in a dataset;

FIG. 5 is a diagram showing an example of how multi-stage processing canbe used to find the next highest value in a dataset;

FIG. 6 is a diagram showing an exemplary process for performing leastsignificant bit interpolation;

FIG. 7 is a flowchart showing an exemplary process for computing acumulative sum of the ranks below the rank of interest;

FIG. 8 is a diagram showing an example of how a cumulative sum may becomputed; and

FIG. 9 is a flowchart of an exemplary process for determining an averageof the values lying between two ranks in a dataset.

DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and isnot intended to limit the invention or the application and uses of theinvention. Furthermore, there is no intention to be bound by any theorypresented in the preceding background or the following detaileddescription.

According to various embodiments, a rank order filter is provided toefficiently yet accurately find the value of a median or other desiredrank in a set of digital data. The filter iteratively processes a set ofdata samples using a series of processing stages, with each stagedetermining one bit of the output value from a single “active” bit ofthe data. The “active” bit is typically the most significant bit thathas not been previously processed. Generally speaking, the processingperformed on each bit involves comparing the effective number of thedesired rank with the number of data samples that remain inconsideration and that have a particular value (e.g., “zero”) for themost significant active bit. If the number of still-in-play data sampleshaving the particular value does not exceed the effective rank number,then the output for that bit is the particular value. Otherwise, theoutput for that active bit will be the opposite of the particular value.Any data samples that do not match the output value at any stage can beexcluded from further consideration, thereby reducing the amount of dataconsidered in subsequent processing.

The various processing stages used to determine the rank order value maybe very efficiently pipelined for implementation in field programmablegate arrays (FPGAs) or similar hardware. Typically, each bit of theinput data set is processed separately in a series of pipelined hardwarestages, with subsequent stages having no need to reconsider the valuesof previously-processed bits. As a result, the active bit data for eachdata sample can be discarded (or ignored) in subsequent processingstages. Additionally, as data samples are identified as having differentbit values than the output value, those samples are removed from furtherconsideration in subsequent stages. This significantly reduces thenumber of gates needed for later processing stages. Even further, manyimplementations allow for efficient sharing of the processing pipelineso that multiple rank values, “next largest” or “next smallest” values,cumulative sums and/or other values may be determined simultaneously.

The exemplary embodiments presented herein may be enhanced or modifiedin many ways to suit a wide array of purposes. To provide just a fewexamples, the iterative nature of the rank order filter allows for veryefficient computation of a “next highest” or “next lowest” value. Thesevalues may be used as an integrity check, for example, or for any otherpurpose. Some embodiments may mathematically combine the output rankvalue with the “next highest” or “next lowest” value to compute a moreaccurate output value, particularly if the data set contains an evennumber of samples (e.g., the median of an even-numbered list of rankswould mathematically fall between two ranks; averaging the two valuesfrom opposite sides of the median would therefore provide a moreaccurate output). Additional details about various embodiments,enhancements and modifications are described in increasing detail below.

Some embodiments may alternately or additional provide for efficientinterpolation of the least significant bit output, thereby greatlyimproving the results of the filter without substantial additionalprocessing. As described more fully below, interpolation of the leastsignificant bit can be used to reduce the effects of quantizationerrors, thereby effectively providing better noise elimination withoutsubstantial additional data processing resources.

Still other embodiments may use the general concepts described herein tomaintain an efficient cumulative sum of the values that are below thedesired rank order (e.g., a “sum to rank” filler). This cumulative sumcan enable a very useful and effective filter that computes an averageof only those values in the data set that lie between two specifiedranks (e.g., between 25% and 75%, or any other desired values). Thisallows extreme or outlying values to be readily excluded from theaverage, while still providing the benefits of an averaging filter. Anynumber of other benefits and features may be provided in many differentalternate but equivalent embodiments.

The various systems and techniques described herein may find use in anynumber of settings. For convenience, the following discussion mayemphasize image and signal processing applications, such as those usedin identifying objects in digital images. Equivalent systems andtechniques, however, may be applied in any other setting that usessignal processing, image enhancement, background smoothing and/or otherprocessing. Moreover, the particular parameters described herein (e.g.,mathematical or logical values, values of constants, sizes and shapes ofdata sets, and/or the like) are purely exemplary. Indeed, the simpleapplication of conventional digital logic principles could produce awide array of equivalent embodiments. For example, references such as“determining if the number of zeros is greater than a threshold” may, insome situations, be equivalently recast using conventional logicalconstructs as “determining whether a number of ones is less than thethreshold”. Similar modifications may be made to much of the particulardigital logic described herein. Many other implementations andembodiments may use any number of different but equivalent values,algorithms and/or other parameters as desired.

Turning to the drawing figures and with reference now to FIG. 1, anexemplary system 100 for processing a data set no having any number ofdata values 102A-J suitably includes an appropriate data processingsystem 114 that provides output(s) 120, as desired. Generally speaking,data processing system 114 applies one or more rank order filters 135A-Cto the input dataset 110 to identify the value of a median or other rankin the dataset no, or any other outputs 120 that may be determined usingthe rank order filter(s) 135A-C as desired. A bounded average of thevalues 102 in dataset no lying between two identified ranks, forexample, could be efficiently calculated and provided as an output 120in some embodiments.

Dataset 110 is any grouping or collection of data samples 102A-J thatcan be processed within system 100. Data samples 102A-J in dataset nomay each represent sample values associated with any measured, computedor other quantity, for example. As mentioned above, rank order filters135A-C are widely used in processing signal and image data, such aspixel intensities of digital images. Equivalent embodiments, however,could be formulated that use any sort of data collection, processingand/or output features that are appropriate to different types ofsampled data 110 other than digital imagery. The various systems andtechniques described herein could be equivalently used to processsamples 102A-J representing data of any sort, such as RF signals,measurements of any environmental or industrial condition (e.g.,temperature, pressure, humidity, or other conditions), time series dataand/or any other type of data as desired. Further, data processing insome embodiments may be performed on multiple datasets 110 in anymanner. Data samples from separate datasets no may be inter-combined,for example, as desired.

Processing system 114 implements one or more rank order filters 135A-Cin any manner. As noted in greater detail below, various embodiments useiterative bitwise processing to sequentially identify output bits of aparticular data value 102-I that corresponds to a median or otherdesired rank of dataset no. The iterative processing may be pipelined orotherwise implemented in a manner that makes efficient use of hardwareand/or software resources. Various embodiments may simultaneously orotherwise execute multiple rank order filters 135A-C on a common datasetno, since the various techniques do not disturb the dataset no duringprocessing. Moreover, a set of delay lines or other input signals can beshared between multiple rank calculations, as described in more detailbelow. This allows for much more compact processing than mostconventional techniques since a common set of input data arriving on asingle set of input lines can be simultaneously processed to arrive atmultiple rank values, if desired.

To that end, many of the techniques described below simply append (orotherwise associate) one or more data flags 111 to each data value102A-J to indicate whether the value 102 remains in consideration forfurther processing (“in play”), and/or to otherwise indicate the statusof the particular value 102 for subsequent processing. Variousembodiments may use data flags 111 to indicate any number of differentstates in any manner, as described more fully below. Examples of some ofthese states might include, for example: “in play”, “next highest”, “outof play high”, “out of play low”, and/or the like. Since the data statesare indicated using the data flags in, there is typically no need todestroy or otherwise modify the input data itself. This non-destructivefeature can allow the common input received at one set of delay lines tobe propagated throughout multiple rank filters. Since each rank filtersimply uses additional bits to track the state of the data as itpropagates through the filter, multiple rank filters (each with its ownstate bits) can simultaneously process the same input data. This conceptmay be modified and/or expanded as desired.

Processing system 114 is any data processing system that includesappropriate hardware, software, firmware and/or combination thereof forprocessing dataset no as described herein. In various embodiments,processing system 114 is at least partially implemented in software orfirmware that can be stored in any conventional memory 118 or massstorage, and that can be executed on any conventional processor 113. Tothat end, processing module 114 may be implemented in this example usinga personal computer, workstation or the like that is based upon generalpurpose computing hardware 104 and that executes software in any format.In other embodiments, processing module 114 is partially or entirelyimplemented using specially-designed processing, data storage and/orother circuitry 117, such as any sort of hardware designed fordeployment in aerospace, maritime, industrial, battlefield and/or otherdemanding environments. In various embodiments, certain features ofprocessing module 114 are partially or entirely implemented usingprogrammable logic devices 117 such as any sort of field programmablegate array (FPGA) or other configurable gate array (CGA), applicationspecific integrated circuit (ASIC), programmed array logic (PAL), and/orthe like. Any number of equivalent embodiments may be designed andimplemented using any sort of hardware 104, software, firmware and/orother digital processing logic as desired.

Data processing system 114 also includes appropriate input/outputfeatures 116 to receive manual or automated data inputs, and to provideoutput 120 as desired. Data may be input from a data acquisition moduleof any sort (e.g., an interface to a camera, radio receiver, sensor orthe like), or from any other source. I/O features 116 may also allowoutputs 120 to be provided to a data network (e.g., via a conventionalnetwork interface), to a display, to a data file in any format stored ondata processing system 114 or elsewhere, to a separate computing systemor process executing on data processing system 114 or elsewhere, and/orto any other human or automated recipient, as desired.

Generally speaking, then, data processing system 114 includesappropriate hardware 104, software and/or firmware to implement one ormore rank order filters 135A-C. Each filter 135A-C suitably receives adataset 110 of values 102A-J from any internal or external source,processes the dataset no to identify a value of a particularly-desiredrank, and provides the identified value as an output 120. Additionaldetails of several exemplary embodiments are provided below.

FIGS. 2A and 2B show two exemplary processes 200, 201 (respectively) fordetermining a rank order value from a set 110 of data samples 102A-J,appropriate. FIG. 2A describes a process 200 in which the number of“zero” values is evaluated for each active bit in the data set, and FIG.2B shows an equivalent process 201 in which “one” values are evaluated.Each process 200, 201 can be readily implemented in hardware using avery efficient number of logic gates, or that can be efficientlyexecuted in software or firmware, as desired. Note that the particulartechniques described in FIGS. 2A-B could be used in any application inwhich a median or any other rank order value is desired.

As shown in FIGS. 2A-2B, processes 200, 201 for determining one or morerank order values suitably include the broad steps of initializing eachof the samples to identify samples that are still in consideration (“inplay”) for further processing (function 202) and identifying the desiredrank order of the desired value (function 204). A bit analysis routineis then repeated (functions 206-220) for each of the active bits in thesamples to identify the desired rank, as described more fully below.

The repeated stages 206-220 may be readily pipelined for simultaneousexecution in some embodiments to create a relatively efficient hardwareor software implementation. That is, various iterations of looping206-220 may be carried out at least partially simultaneously usingparallel hardware 104, software and/or other logic so that results canbe obtained relatively quickly.

Processes 200, 201 begin after the dataset 110 is received at aprocessing device 114 as appropriate. As noted above, data values 102A-Jmay represent any sort of data, and may be received from any source thatis internal and/or external to processing device 114. Process 200 isgenerally hardwired or otherwise initialized with a data word length, oranother indicator of the number of digital bits in each data value102A-J. Typically, stages 206-220 will be repeated for each data bit,although other embodiments may be differently configured as desired.Some implementations may not consider all of the least significant bits,for example, if an approximation of the desired rank value is sufficientfor the particular application.

Function 202 illustrated in FIGS. 2A-2B initially identifies all of thedata samples 102 to be processed as “in consideration”, or “in play”.“In consideration” or “in play” in this sense simply reflects that thesample value has not yet been determined to be above or below thedesired rank, so further processing on the data sample 110 is warranted.Samples may be indicated as “in play” by simply setting a bit or otherflag in that is associated with the particular value 102, asappropriate. In various embodiments, the “in play” data set may excludeany samples 102 that are intentionally excluded. Samples resulting fromdefective pixels in an image processing application, for example, couldbe readily excluded by simply indicating that the samples 102 associatedwith the defective pixels are no longer “in play”, and the adjusting thedesired rank to account for the excluded samples 102. Other samples 102could be initially identified as “not in play” for any other reason toconveniently exclude these values from further processing, as desired.

Initialization may also include determining the rank order of thedesired value (function 204). The desired rank may be expressed withreference to the lowest value (“the bottom”) of the dataset no, withrespect to the greatest value (“the top”) of dataset no, or with regardto any other reference. The desired rank order may be hard-coded intosome implementations, although other implementations may be configurableas desired. In some embodiments, the rank order of the desired value issimply the central median value of an ordered list (e.g., the eighthsample in a seventeen-sample list), which can be readily determined bysimply counting the number of samples that will be processed (ignoring,if appropriate, any values excluded from processing, e.g., any “deadpixels” or other values excluded by mask 302). This number of samples tobe processed may correspond to the number of samples that are initiallyin play, as desired. When an even number of samples is present, the rankorder of a median may be initially assumed to be the lower of the twocentral values (e.g., to accommodate for any upward bias created byclutter points or the like) in some implementations. Alternatively, theupper value could be used, or the two central values could be averagedor otherwise processed as desired. Any indication of the rank order thatis to be sought could be used in any number of alternate embodiments.Process 200 is not limited to computation of median values, then, butrather could be used to identify any rank that may be desired. Further,process 200 may be used to simultaneously identify multiple rank values,with each desired rank having an associated set of “in play” flags andassociated rank order registers.

Functions 206-220 may be sequentially and iteratively repeated for eachof the digital bits used to represent the sample values, beginning withthe most significant bit (MSB) and proceeding to the least significantbit (LSB). If the samples are represented by sixteen-bit values, forexample, the loop encompassing functions 206-420 may be repeated sixteentimes, once for each bit. The bit that is considered during anyparticular iteration is typically the most significant bit that has notyet been processed; this bit is referenced herein as the “active bit”.While some embodiments may repeat loop 206-220 for every bit in the datasamples, other embodiments may simply execute the process for the mostsignificant bits (e.g., the most significant eight bits), or in anyother manner, as desired.

At the beginning of each iteration of the loop 206-220, a count is taken(function 206) of the number of samples that are both in play and thathave an active bit value equal to a first value. In the example shown inFIG. 2A, the “first value” is a logic low (“0”) value, although otherembodiments could be equivalently created that would instead compare thebit of interest to a logic high (“1”) value, as shown in FIG. 2B. Insuch cases, the sense of the rank may be specified from the opposite endof the list of values, and/or other modifications may be made as well.

This count 206 is then compared to the desired rank order to determinethe value of the active bit in the desired sample (function 208). If thenumber of in play samples with an active bit equal to the first valueexceeds the number of the desired rank order, then the value of theactive bit in the desired sample must be equal to the first value(function 210). Conversely, if the number of in play samples with anactive bit equal to the first value is less than the desired rank order,then the value of the active bit in the desired sample must be theopposite of the first value, that is, a “1” as illustrated in FIG. 2A(function 214).

FIG. 2B similarly shows that the number of ones remaining in play can betracked (function 206B), and this number can be compared to anappropriate desired rank order value (function 208B). In the example ofFIG. 2B, the desired rank may be expressed in relation to the greatestrank (e.g., “Xth rank from the top of the list”). If the desired rank isinitially expressed in reference to the bottom of the list, then anadjusted desired rank may be computed in function 204 and/or function208B based upon the total number of in play samples 102 and theparticular rank being sought. Equivalent embodiments, however, maysimply use different schemes for establishing the desired rank, asdesired.

The samples that have active bits differing from the active bit of thedesired value can be identified as no longer in play (functions 212,216). In function 212 as illustrated in FIGS. 2A-B, for example, theactive bit of the desired sample is determined to be a “0”, so anysamples with an active bit equal to “1” can be treated as no longer inplay. Similarly, function 216 as illustrated in FIGS. 2A-B would changethe “in play” settings of any samples that had an active bit value equalto “0” after it was determined that the desired sample has an active bitequal to “1”. Subsequent iterations of loop 206-220 would therefore notneed to consider samples that were flagged as no longer in play, therebyspeeding the computations, and reducing the amount of circuitry neededto process subsequent stages.

Additionally, in the embodiments shown in FIGS. 2A-B, the rank order ofthe desired value may be adjusted (function 218) to account for the anysamples that were changed to “not in play” in function 216. Thisadjustment reflects the position of the desired value within the samplesremaining in play. In FIG. 2A, for example, function 218A shows that thedesired rank is increased to reflect that samples 102 with a “zero”value will no longer be in play. FIG. 2A equivalently shows function218B as decreasing the desired rank to reflect that samples 102 with a“one” value will no longer be in play. This adjustment of the

While FIGS. 2A-B show functions 218A-B as adjusting the rank order valuethat was determined in function 204, equivalent embodiments may use aseparate variable to represent the rank order in comparison 208 and inadjustment functions 218 so that the initially-determined rank order maybe preserved for subsequent processing. Various embodiments, forexample, could add an additional bit or other flag 111 to track whethereach sample value taken out of play is deemed to be higher or lower thanthe desired rank. This additional flag 111 may obviate the need toadjust the rank order in function 218 in such embodiments.

Again, the particular logic values illustrated in FIGS. 2A-B could bereadily toggled or otherwise logically adjusted in any number ofequivalent embodiments. For example, some embodiments could adjust the“greater-than or equal” comparison shown in function 208A to be a “lessthan” comparison in which the “rank order” represents a count downwardfrom the top of the list, rather than a count up from the bottom of thelist as shown in FIG. 2A. In such cases, the rank adjustment function218 would be performed in the loop that contains functions 210 and 212rather than the loop that includes functions 214 and 216 as shown.Further, equivalent embodiments could count the number of ones insteadof the number of zeros. FIG. 2B shows one example of a technique thattracks the number of ones. Generally speaking, then, the example shownin FIG. 2A determines the rank order value by counting zeros from the“bottom” of the dataset, whereas the example shown in FIG. 2Bequivalently determines the rank order value by counting ones from the“top” of the dataset. Again, equivalent embodiments may count eitherzeros and/or ones from either the top and/or bottom of the dataset bysimply selecting appropriate comparisons performed in functions 206 and208 and adjustments in function 218. Many other different but equivalentembodiments could be formulated as desired.

Some embodiments may include additional or alternate features. Forexample, various embodiments suitably track a “next highest” or “nextlowest” value (function 213) that may be useful in computing a blendedmedian or other result. If dataset 110 contains an even number of ranks102, for example, it may be desirable to average the values of twocentral ranks 102 to arrive at a median value rather than simplyselecting between the two central ranks. Similar concepts may be appliedto ranks other than the median as well. Additional detail about anexemplary “next highest” feature is provided below with respect to FIGS.4-5, and other embodiments may use different techniques as desired.

Still other embodiments may alternately or additionally compute acumulative sum (function 215) of the values 102 that are less than therank of interest. This cumulative sum feature may be efficientlycalculated within loop 206-220, and may be very useful in computingclipped median functions, bounded mean functions or similar functionsthat compute linear averages of values lying between two ranks, asdescribed more fully below. An exemplary process to efficiently trackcumulative sums within loop 206-220 is described below with respect toFIGS. 7-8.

After all of the desired bits are processed (function 220), the desiredvalue may be output as desired (function 222). The desired value may beoutput 120 as an argument returned from a programming function, routineor other procedure in some implementations. Alternately, the desiredvalue may be latched or otherwise output from a hard-wired digital logiccircuit (e.g., a CGA, ASIC or the like) in other implementations. Otherembodiments may provide the output value in any format using any sort ofhardware, software, firmware and/or other logic, as desired.

Some embodiments may provide additional post-processing on the output120, as desired. For example, some embodiments may interpolate orotherwise smooth the output 120 (function 221) to reduce the effects ofinput quantization or the like. Additional detail about an exemplaryinterpolation process is described below with respect to FIG. 6,although other embodiments may use other techniques as desired.

Generally speaking, each of the various steps in processes 200, 201 maybe performed by computing hardware, firmware and/or software executingin any data processing environment. In an exemplary embodiment, some orall of these processes are implemented in software instructions that areassociated with processing module 114 that can be stored in memory 118or in any other mass storage, and that can be executed on processor 116.Other embodiments may be implemented in dedicated processing hardware,firmware and/or other means as desired, including any sort of commongate array, ASIC, or other programmed or programmable digital logic 117as desired. The techniques described in FIG. 2 may be very efficientlyimplemented in CGA structures by using pipeline structures to implementthe iterative multi-bit processing.

FIGS. 3A and 3B illustrate the “pipelined’ nature in which a rank ordervalue may be determined. With reference to FIG. 3A, a sort of “bitcascade” can receive any number of data samples 102A-B as an input, thenprocess the data through a series of pipeline stages 321-331 in whicheach active bit of the data set is independently evaluated. Typically,processing begins with the most significant bit (MSB) in stage 321, andprogresses through each stage until the least significant bit (LSB) isprocessed at stage 331. At each stage 321-331, one bit of the outputvalue 120 is determined based upon a comparison of the currently-desiredrank with a count of the data samples 102 having a particular value forthe active bit 310. After the value of the output bit is determined, anydata samples 102 that have active bit values that differ from thedetermined output value can be excluded from further consideration, andprocessing continues to the next stage. Processing then continues untilall of the stages are complete, and the result can be provided as anoutput 120.

The pipeline structure shown in FIG. 3A can be readily implemented inconfigurable gate arrays (CGAs) or similar hardware. After a particularactive bit has been evaluated, it does not need to be considered againin future stages, so the more significant bits can generally bediscarded (or at least ignored) after they have been processed. Thisgreatly reduces the number of logic gates needed to process thesubsequent steps in comparison to the number that would be needed toprocess each bit at every stage.

Further, the data in each sample 102A-B does not need to be modified ordestroyed at any particular processing stage 321-331. In contrast toother techniques that modify the bit values of samples underconsideration, the only data that is modified at each stage of variousembodiments is the “flag bit” or other in-play marker for each datasample 102. As the data samples 102A-B are fed through the dataprocessing pipeline, then, multiple comparisons or other actions may besimultaneously and/or sequentially performed on the data withoutaffecting later processing stages. As a result, some embodiments mayimplement multiple simultaneous filters 135 by simply adding additional“in play” bits in for each data sample 102, as well as additional outputbits for each desired output.

The general pipeline structure shown in FIG. 3A may be modified orenhanced in any number of ways. Various embodiments may use “look ahead”techniques, for example, to further reduce computation times. In manyimplementations, it can be expected that a substantial amount ofprocessing time may be consumed in counting the number of in-play bitshaving the desired value. Often, this count will be performed usinglogic similar to a conventional mutli-bit adder, a hamming distancecalculator, or the like that can be time limited by ripple-carry delayand other factors. This delay may be reduced, however, by using carrylookahead techniques, by pre-calculating results for different possibleoutcomes in prior stages, by predicting results of prior stages (e.g.,by predicting which samples 102 may remain “in play”), or using anyother techniques. In such embodiments, the total time available topropagate results increases by the number of look-ahead stages, andselection of a final answer may be performed using a relativelylow-latency multiplexer. Other techniques for streamlining or otherwiseimproving the performance of the pipelined structure may be implementedin any number of alternate but equivalent embodiments.

FIG. 3B shows a more detailed example in which the value of a desiredrank 315 is determined for an exemplary dataset 110 that includes sevendata samples 102A-G each having five data bits 301-305 that are seriallyconsidered in five processing stages 321-325. In this example, the rank315 to be identified is the fourth rank, which happens to correspond tothe median of this particular dataset 110. Equivalent embodiments,however, could seek out other ranks other than the median. This examplecould be readily adapted to consider other datasets 110 having any wordlength and/or any number of samples 102 as desired. Also, the seven datavalues are arranged in numerical order in FIG. 3B for clarity and easeof understanding. In practice, it the various values 102 do not need tobe sorted or otherwise ordered prior to processing, since the in-playflag 111 is able to identify any of the various samples 102 that remainin consideration regardless of that sample's position within dataset110.

As noted above, the process is initialized so that the desired rank 315is identified, and so that all of the samples 102A-G are initiallyflagged as “in play”. In this example, an in-play bit 111 is set forsamples 102 that remain in play. The in-play bit 111 is then clearedwhen the associated sample 102 becomes no longer in play. Otherembodiments may use different signaling or data representation schemes,as appropriate.

In stage 321, active bit 310 is the most significant bit (MSB) 301 ofthe dataset 110. At this initial stage 321, the rank being sought (#4)is greater than the number of zeros (2), so it can be readily deducedthat the output bit for stage 321 will be a “1”. That is, the soughtrank 315 is greater than the number of zeros, so the output value of thedesired rank must have a “1” in the MSB position 301. This value of “1”may be provided as the most significant active bit of the output 120, asdesired. Further, all of the values 102 in dataset no that do not have a“1” as the active bit 301 (values 102F-G in this example) can be removedfrom further consideration by clearing the in-play bit in for thosevalues. The count for the desired rank 315 is adjusted to account forthe two values 102F-G that are no longer in play, and processing for theMSB 301 is complete.

Stage 322, then, seeks the second rank out of the five values 102A-Ethat remain in play by considering the next active bit 302. In theexample of FIG. 3B, three values 102C-E have “zero” values on bit 302,so the number of zeros (i.e., 3) exceeds the sought rank (i.e., rank #2)for this stage 321. This means that the output bit for stage 321 is azero, and that values 102A-B can be excluded from further considerationby clearing their in-play bits 111.

In stage 323, all three samples 102C-E that remain in-play have a “1”value on bit 302. The output bit for stage 323 is therefore a “1”, andno values 102 are excluded from play. Since no values are excluded, thesought rank is not changed, and processing continues to consider thenext bit.

Stage 324 continues to seek the second rank of the values 102C-E thatremain in play by considering the fourth bit 304 as the active bit 310.In this example, value 102C has a “1” on bit 303, and values 102D-E have“0” values on bit 304. The output bit for stage 323 is therefore a zero,and value 102C (which has a “1” on bit 304) is excluded from furtherconsideration by clearing the in-play flag 111.

In the final stage 325, then, the sought rank (rank #2) is equal to thenumber of zeros since both remaining values 102D-E are identical to eachother. The output bit for stage 325 is therefore a zero, and the outputvalue 120 of the fourth rank in dataset 110 is properly shown to be“10100”. Again, this illustrative example may be supplemented orotherwise modified in any number of alternate embodiments.

FIG. 4 shows an exemplary process 400 for tracking the “next highest”value during the iterative portion of the rank order filter. In someimplementations, functions 402-410 may be implemented within function213 of FIG. 2, although other embodiments may implement “next highest”features in any other manner.

Typically, each value 102 will be associated with an additional bit orother flag in that can be set (or cleared, as desired) to indicate whenthe associated value 102 is potentially the next-highest value. The“next highest” bit 111 is initially clear for each value 102 until aprocessing stage 321-325 identifies values 102 with different bit valueson the relevant active bit for that stage.

If the active bits for all of the in-play values 102 are the same(function 402), then the previous “next highest” settings are maintained(function 404). If the active bits for the in-play samples 102 differ,however, then potential “next highest” values 102 can be determinedbased upon the value of the output bit provided from that processingstage 321-325. If the output bit is a zero (function 406), for example,then the next highest values can be determined to have the same value asthe in-play samples 102, but with an active bit value of a one insteadof a zero (function 408). Conversely, if the output value for the activebit is a one (function 408), then the more significant bits of thenext-highest samples 102 will remain the same as the previous setting,if these bits are all identical to each other (function 410). If theactive bits for the next-highest value are not identical, however, thenthe lower (zero) value can be maintained, and next-highest flag 111 canbe cleared for those samples 102 having the higher (one) active bitvalue (function 411). Process 400 is repeated on each iteration of loop206-220 (FIG. 2), as desired (function 412).

FIG. 5 provides an illustrative example of process 400 in which the“next highest” sample 102 that is greater than the fourth rank in thedataset no is sought. As noted in the discussion of FIG. 4, potential“next highest” samples 506 can be tracked with a “next highest” flag111, as desired. As processing proceeds though stages 511-516 toconsider bits 301 to 306 (respectively), the number of samples 102 thatremain in-play 504 decreases until the value of the sought rank 315 isidentified. Similarly, samples 102 that are potentially “next highest”decrease until the desired value is identified. In-play samples 504 andnext-highest samples 506 may be identified using separate flags 111, asappropriate.

As noted previously, “next-highest” samples 506 may not be recognizeduntil at least stage 511-516 recognizes two different values of thein-play samples 504. In the first stage 511 shown in FIG. 5, the outputbit of the third rank is a “zero”, but four samples 102A-D with activebit values equal to one are also present. Samples 102E-F with a “zero”value on bit 301 are therefore flagged as “in-play” 504, and samples102A-D having an active bit 301 equal to a “1” are flagged aspotentially “next highest” 506 for processing in stage 512. Samples thatare neither in play nor “next highest” may be further marked asout-of-play 502, as desired.

In stage 512, each of the in-play samples 102E-I has a common “zero”value for the active bit 302, so the more significant bits of thenext-highest samples 504 do not change. Because the values of bit 302differ between the next-highest samples, however, the samples 102A-Bhaving the higher bit values can be excluded from further consideration.That is, since samples 102C-D are already identified as being greaterthan the in-play values, it can be deduced that the still greater valuesof samples 102A-B are not the “next highest”. These samples 102A-B cantherefore be considered out of play and no longer potentially “nexthighest”, as indicated by region 502B of FIG. 5.

In stage 513, the output bit is a zero even though two in-play samples102E-F have active bits 303 equal to one. These samples 102E-F aretherefore identified as potentially next-highest 506, and samples 102C-Dare removed from further consideration (region 502B). Samples 102C-Dremain as potentially next-highest 406 through stage 514 because theoutput of stage 514 is a one, and because samples 102C-D both have thesame value for bit 304. In stage 515, the equal values of bit 305 forsamples 102G-H would dictate no change in next highest values 506,although sample 102E can be excluded, since it has a greater value thansample 102F. Sample 102F is then confirmed as the next-highest value 506when the active bit 306 of stage 516 is identical for the remainingin-play samples 102F-G. The output 120 from this example thereforeindicates that the sample 102G value of 000101 the sought rank value315, and the next highest value is sample 102F, a value of 001100.

Various embodiments may equivalently provide a “next lowest” function orthe like using similar techniques. A “next lowest” function may beimplemented using techniques similar to those illustrated in FIGS. 4 and5, but with the various comparisons modified to seek the lower valuerather than the higher value. The “next highest” and/or “next lowest”functions may be used as an integrity check on the rank order filter insome implementations, or for any other purpose. Other embodiments mayaverage the sought rank with the next highest or next lowest value(e.g., if desired to compensate for an even number of samples 102 in adataset 110), as desired.

Various embodiments may provide post-processing (function 221 in FIG. 2)in any manner. FIG. 6, for example, shows an exemplary process 600whereby the least significant bit (LSB) of the identified rank ordervalue is interpolated with respect to other ranks having the same orsimilar values to reduce the effects of quantization/sampling issues,and to improve the resolution of the output 120. In such embodiments,degradations in signal-to-noise ratio (SNR) that are due to inputquantization can be effectively smoothed by simply interpolating the LSBacross an appropriate range. In the example of FIG. 6, the output bitfrom the LSB is simply compensated based upon the number of equivalentvalues that remain in-play in the final stage of rank order processing.If the output rank is found to be the middle of a range of equal values,for example, then the LSB can simply be output as-is. Plot 602 shows anexample wherein five “zeros” remain in play in the final stage of LSBprocessing. If the output rank 315 is the central (third) rank of thefive zero values, then the output would remain “zero”, as appropriate.If the output rank 315 was not the central rank, however, then theoutput could be scaled to reflect the position of the output rank 315with regard to the total number of equal values. If the output rank wasthe first rank of five “zero” outputs, for example, then the output maybe scaled downward by the equivalent of a half bit value or so.Conversely, if the output rank was the fifth rank of the five “zero”values, then the output may be scaled upwardly by a half bit or so, asdesired. Similar scaling could be applied if the output is a one, withthe output rank's relative position within the set of equal outputvalues determining the scaling of the output value as shown in plot 604.This scaling effectively implements a

Equation 606 shows an algebraic example of how the output rank can bescaled based upon the number of equal in-play values in the active LSB;other equations or techniques may be equivalently applied, as desired.In the example of FIG. 6, however, the output rank 315 and the number ofzeros and/or ones is already determined as part of the output logic, sothe additional computation to provide an interpolated output may not besignificant relative to the other data processing provided within dataprocessing system 114.

This interpolation can dramatically improve the results obtained by therank order filter, as shown in graphs 650 and 660. Graph 650 shows thenormalized average noise resulting from a median filter that includesinterpolation as described for various levels of quantization in thesample data. In this example, the optimum operating point would be nearpoint 652, where the quantization most closely approximates the level ofnoise in the dataset. At noise levels to the left of point 652, noisequantization is large relative to the noise level itself, and thenormalized average noise itself increases sharply as the quantizationincreases. Although noise also increases (toward an asymptote of 1.25 inthis example) as quantization levels decrease to the right of point 652,the increase is less dramatic than to the left. This supports theconclusion that quantization levels should be designed to be close tothe noise level. Moreover, graph 650 clearly supports the relativelysurprising conclusion that in this case under-quantization is generallypreferred to over-quantization.

Turning to graph 660, an exemplary plot of the normalized average noiseis shown for various types of filters and different numbers of samples.From graph 660, it can be readily seen that the performance 662 of theadjusted median filter is relatively constant for various sample sizes,and only slightly less favorable than the performance 663 of acomparable mean filter. Interestingly, the performance 662 of theadjusted median filter with quantized inputs was uniformly better thanthe performance 664 of the median filter with real-valued inputs. Thisleads to the relatively surprising result that the interpolationdescribed above not only overcomes the effects of quantization error,but does better than a real-valued median filter in someimplementations. In particular, graph 660 demonstrates the unexpectedconclusion that it may be beneficial in some situations to increase thecoarseness of the input quantization before filtering when the noise istoo much larger than the LSB. That is, lower resolution input may, insuch cases, provide a more accurate result than higher resolution input.

As noted at the outset, various embodiments may additionally oralternately compute bounded averages of rank values lying between toparticular ranks of the dataset. This average, while useful insummarizing pixel values or other data samples 102 while excluding theeffects of relatively high (or low) magnitude noise signals, haspreviously proven to be relatively difficult to implement, particularlyin programmable gate arrays or other custom hardware.

Various embodiments therefore supplement the general rank order processdescribed in conjunction with FIGS. 2-3 above by maintaining acumulative total of the values that lie below the desired output rank.FIG. 7 shows one technique for efficiently summing the cumulative valuesof the samples 102 that lie below the desired rank 315. Such a process700 may be implemented in the context of function 215 of FIG. 2, or inany other manner.

As shown in FIG. 7, a cumulative sum is initially set to zero (function702). This sum is updated during processing to reflect the additionalvalues stored in the active bits, particularly in the samples 102 thatare not in play and that are below the rank of interest. To that end,samples 102 may be associated with one or more additional bits or otherflags in that indicate that the sample is both out-of-play and below theselected rank 315 (function 704). Various embodiments may use two bits111 to represent up to four states (e.g., “in play”, “out of play-high”,“out of play-low”, and “next highest”). Other embodiments may useadditional bits in for better data integrity, ease of signal processing,and/or for any other purpose. The status bits set in function 704therefore indicate those ranks that are both out of play and below thetarget rank 315.

The cumulative sum is updated on each processing stage to reflect thetotal values of ranks that are less than the target rank 315 (function706). In various embodiments, this cumulative sum can be maintained bysimply multiplying the previous cumulative sum (i.e., the sum for themore significant bits that have already been accumulated in earlystages) by two, and then adding the ones that are present in the activebit of the relevant “low and out of play” ranks. The prior sum ismultiplied by two (or logically shifted one bit to the left) to reflectthat the prior cumulative sum was calculated from bits that are moresignificant than the active bit. The total number of “ones” from activebits of the low out-of-play ranks is then added to the shifted sum toreflect the value of the then-current active bit. Since addition is acommutative property, it is not typically necessary to track theparticular values that have “zero” or “one” values for the active bit;it is sufficient to simply note the total number of ones occurringwithin the relevant ranks, and then add this number to the cumulativesum.

If the output bit for the then-current active bit is a “one” (function708), then additional values will be added to the cumulative sum toreflect the total value of the additional ranks that have newly-become“low out-of-play” ranks during the current processing stage (function710). In various embodiments, the value of these additional ranks simplycorresponds to the prior output values from the previously-consideredstages multiplied by two (or logically shifted a bit to the left), andthen further multiplied by the number of previously in-play ranks thathave zeros in the active bit.

The cumulative sum is updated on each iterative processing stage(function 712) so that the cumulative sum reflects values from each bitof the dataset 110. Status bits 111 are updated following processing ofeach stage (function 714) to reflect any newly-out-of-play ranks, andthe value is updated as appropriate until each bit has been considered.Various embodiments may further add scaling or other adjustments afterall of the bits have been considered, as desired (function 716). Someimplementations may add the value of the target rank 315, for example,as desired for the particular application.

FIG. 8 shows two exemplary scenarios 801, 802 in which a cumulative sum805 is calculated during the iterative identification of a target rankvalue 315. In the scenario 801 toward the left of FIG. 8, the outputvalue for bit 306 is a zero, so no additional ranks are added to the “inplay low” section 502A. The cumulative sum 805 from the prior processingstage generally includes the values of the more significant bits801-804, so this prior cumulative sum 805 would be multiplied by two (orshifted to the left) and the values of all of the low out-of-play ranksare added. In the example shown in scenario 801, only two lowout-of-play ranks have “one” values in active bit 306, so a value of twowould be added to the prior cumulative sum 805. The in-play ranks havingan active bit 306 equal to one are removed from play in subsequentiterations, but these ranks have a value that inherently exceeds that ofthe target rank 315. These ranks are therefore added to the out-of-playhigh section 502B, and the values are not considered in the cumulativesum 805.

Scenario 802 illustrates a similar situation when the active bit 306provides an output value of one. In this instance, the in-play values102E and 102F are flagged as no longer in play, and as being less thanthe target rank 315. In addition to adding the values from active bit306, then, the cumulative sum needs to consider the values added byranks 807. Because these ranks 807 were previously in play, however, themore significant bits of these values will be known to be equal to theoutput values that have been determined in the prior iterations.Further, it is known that the number of ranks 807 being added is equalto the number of previously in-play ranks 102 having zero values in theactive bit 306, which is often a quantity that has been previouslycalculated. By simply multiplying the number of in-play zeros by thevalue of the output bits (scaled as necessary), then, the full value ofthe newly-added ranks can be conveniently considered. Many otherembodiments may supplement or modify this process, as desired.

The cumulative sum feature may be used for any number of differentpurposes, such as to compute a bounded average value for certain valuesin dataset 110 that lie between two particular ranks. FIG. 9 shows anexemplary process 900 for finding a bounded average. Generally speaking,two different rank values 315 are identified using rank order filters135A-C or the like, and cumulative sums 805 for each rank are computedas described above (functions 901, 902). The two different values 315and their cumulative sums may be computed in series or parallel, asdesired.

To compute the average value of the ranks 102 falling between theidentified upper and lower ranks, then, the cumulative sum of the lowerrank is subtracted from the cumulative sum of the upper rank (function904). This difference may then be divided by the number of active ranksthat separate the two values to arrive at the average of the interveningranks. This average may be provided as output 130 or the like, asdesired (function 906). The particular algorithms or techniques used tocomputing the bounded average may be modified or supplemented asdesired.

Various systems and techniques for processing data are thereforedescribed. As noted at the outset, these techniques and systems may bevariously applied in any military, industrial, commercial, personal orother setting for image enhancement, target/object recognition, signalprocessing, filtering and/or other benefits as appropriate. Any numberof modifications and enhancements could be formulated from the variousexamples described herein.

As used herein, the word “exemplary” means “serving as an example,instance, or illustration”. “Exemplary” embodiments are not intended asmodels to be literally duplicated, but rather as examples that provideinstances of embodiments that may be modified or altered in any way tocreate other embodiments. Any implementation described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other implementations.

While the foregoing detailed description will provide those skilled inthe art with a convenient road map for implementing various embodimentsof the invention, it should be appreciated that the particularembodiments described above are only examples, and are not intended tolimit the scope, applicability, or configuration of the invention in anyway. Various changes may be made in the function and arrangement ofelements described without departing from the scope of the invention andits legal equivalents.

1. A method executable by data processing hardware to find an outputvalue of a desired rank in a set of data samples, wherein each of thedata samples comprises a set of digital bits each having either a firstvalue or a second value and wherein the output value is represented by aset of output bits each having either the first value or the secondvalue, the method comprising the steps of: receiving each of the datasamples in the data set at the data processing hardware; for each of thedigital bits, sequentially treating the bit as an active bit andcomputing a value of one of the output bits based upon the values of theactive bits of the data samples, wherein the computing for each activebit comprises: determining the value of the output bit based upon acomparison of the desired rank with a count of the data samples thatremain in consideration and that have a value of the active bit equal tothe first value; if the comparison indicates that the value of theoutput bit is the first value, then excluding all data samples havingthe active bit equal to the second value from further consideration; andif the comparison indicates that the value of the output bit is thesecond value, then adjusting the desired rank and excluding all datasamples having the active bit equal to the first value from furtherconsideration; and after computing the output values of each of theoutput bits, outputting the output value from the computed output bits.2. The method of claim 1 wherein the computing comprises: determiningthe count of the number of data samples that remain in consideration andthat have the value of the active bit equal to zero as the first value;if the count is less than the desired rank, providing a one as the valueof the output bit, treating each of the data samples having the value ofthe active bit equal to zero as no longer in consideration, andincreasing the desired rank to account for the data samples that are nolonger in consideration; and if the count is greater than or equal tothe desired rank order, providing zero as the value of the output bit,and treating each of the data samples having the value of the active bitequal to one as no longer in consideration.
 3. The method of claim 1wherein the computing comprises: determining the count of the number ofdata samples that remain in consideration and that have the active bitequal to one as the first value; if the count is greater than or equalto the desired rank order, then providing one as the value of the outputbit, treating each of the data samples having the output bit equal tozero as no longer in consideration; and if the count is less than thedesired rank order, then providing zero as the value of the output bit,treating each of the data samples having the value of the output bitequal to one as no longer in consideration, and decreasing the desiredrank to account for the data samples that are no longer inconsideration.
 4. The method of claim 1 further comprising associatingeach of the data samples in the data set with an inplay bit that isinitially set so that the data sample remains in consideration.
 5. Themethod of claim 4 further comprising excluding at least one data samplefrom the data set by clearing the inplay bit associated with theexcluded data sample prior to the computing step.
 6. The method of claim1 wherein the computing step further comprises tracking a next-highestvalue of the rank order.
 7. The method of claim 6 wherein the trackingstep comprises: determining if all of the data samples remaining inconsideration are equal to each other; if all of the data samplesremaining in consideration are equal to each other, maintaining acurrent next-highest value for the active bit; if all of the datasamples remaining in consideration are not equal to each other, thenmaintaining the current next-highest value for the active bit if theoutput for the active bit is the second value, and otherwise resettingthe current next-highest value to correspond to the outputs of the prioriterations of the computing step for each of the prior active bits withthe second value as the next highest value.
 8. The method of claim 1wherein the computing step further comprises tracking a next-lowestvalue of the rank order.
 9. The method of claim 8 wherein the trackingstep comprises: determining if all of the data samples remaining inconsideration are equal to each other; if all of the data samplesremaining in consideration are equal to each other, maintaining acurrent next-lowest value for the active bit; if all of the data samplesremaining in consideration are not equal to each other, then maintainingthe current next-lowest value for the active bit if the value of theoutput bit is the first value, and otherwise resetting the currentnext-lowest value to correspond to the outputs of the prior iterationsof the computing step for each of the prior bits with the first value asthe next lowest value.
 10. The method of claim 1 further comprisinginterpolating a value of the least significant bit of the output valueprior to the outputting step.
 11. The method of claim 10 furthercomprising, prior to the interpolating, adjusting a quantization levelof the least significant bit.
 12. The method of claim 11 wherein thequantization level is adjusted to match a level of noise in the set ofdata samples.
 13. The method of claim 10 wherein the interpolatingcomprises scaling the output value as a function of the relativeposition of the desired rank within the final run of identical values.14. The method of claim 1 further comprising maintaining a cumulativesum of the active bits of data samples that are below the desired rank.15. The method of claim 14 wherein the maintaining comprises trackingdata samples having values that are less than the value of the desiredrank.
 16. The method of claim 14 wherein the maintaining comprisessetting a flag associated a particular data sample if the particulardata sample is found in the iterative processing step to be below thedesired rank.
 17. The method of claim 1 further comprising, for eachiteration of the computing step, maintaining a cumulative sum of theactive bits for those data samples that are beyond the desired rank. 18.The method of claim 17 wherein the maintaining comprises multiplying thecumulative sum from the previous iteration by two and adding the numberof data samples that are below the desired rank and that have an activebit equal to the second value.
 19. The method of claim 17 wherein themaintaining further comprises, when the output for the active bit is thesecond value, additionally adding to the cumulative sum the value of theoutput bits from the prior iterations multiplied by two times the numberof in play data values having active bits equal to the first value. 20.A computational system to find an output value of a desired rank in aset of data samples, wherein each of the data values comprises a set ofdigital bits each having either a first value or a second value, thesystem comprising: an output interface; and data processing circuitryconfigured to receive the set of data samples, to compute the outputvalue to include one output bit from each active bit in the set ofdigital bits, and to provide the output value from the output bitsprovided for each active bit via the output interface, wherein thecomputing for each of the active bits comprises: determining a count ofthe number of data samples that remain in play and that have the activebit equal to the first value; if the count is not less than the desiredrank, providing the first value as the output bit for the active bit andtreating each of the data samples having the active bit equal to thesecond value as no longer in play; and if the count is less than orequal to the desired rank order, providing the second value as theoutput for the active bit, treating each of the data samples having theactive bit equal to the first value as no longer in play, and adjustingthe desired rank to account for the data samples that are no longer inplay.
 21. The system of claim 20 wherein the data processing circuitryis at least partially implemented in a configurable gate array.
 22. Thesystem of claim 21 wherein the configurable gate array comprises aninput portion configured to receive the set of data samples, a firstrank order filter configured to determine the output value of thedesired rank from the set of data samples, and a second rank orderfilter configured to simultaneously determine a second output value of asecond desired rank from the set of data samples.
 23. The system ofclaim 22 wherein the first rank order filter is configured to maintain,for each iteration of the iterative computing step, a first cumulativesum of the active bits for those data samples that are below the desiredrank and the second rank order filter is configured to maintain a secondcumulative sum of the active bits for those data samples that are belowthe second desired rank.
 24. The system of claim 22 wherein the dataprocessing circuitry is further configured to compute an average ofvalues of the data samples between the desired rank and the seconddesired rank based upon the first and second cumulative sums.
 25. Thesystem of claim 20 wherein the data processing circuitry is furtherconfigured to interpolate a value of the least significant bit of theoutput value.
 26. The system of claim 20 wherein the data processingcircuitry is further configured to adjust a quantization level of theleast significant bit prior to the interpolating.
 27. The system ofclaim 20 wherein the quantization level is adjusted to match a level ofnoise in the set of data samples.
 28. The system of claim 20 wherein thedata processing circuitry is further configured to interpolate the leastsignificant bit of the output value based on the desired rank within thesamples in consideration and based upon the number of data samples inconsideration having a least significant bit equal to the leastsignificant bit of the output.
 29. The system of claim 20 wherein theprocessing circuitry is organized in a pipelined fashion such that eachof the data samples is processed in parallel, and wherein the outputvalue is computed from a series of processing stages each providing oneof the active bits for the output value.
 30. The system of claim 29wherein a most significant bit for each of the data samples is discardedafter each of the processing stages is complete.
 31. The system of claim20 wherein the data processing circuitry comprises an input portionconfigured to receive the set of data samples, a first rank order filterconfigured to determine the output value of the desired rank from theset of data samples, and a second rank order filter configured tosimultaneously determine a second output value of a second desired rankfrom the set of data samples.
 32. The system of claim 31 wherein thedata processing circuitry is organized in a pipelined fashion such thateach of the data samples is processed in parallel by a common series ofprocessing stages each simultaneously providing one of the active bitsof the output value and of the second output value.